Determination of Equilibrium Income in the Short Run - Macroeconomic Equilibrium with Price Level Fixed

Macroeconomic equilibrium when price level is fixed. Based on Determination of Equilibrium Income in the Short Run.

Intercept form of the linear equation

General linear equation:

\[Y = a + bX\]

X and Y are variables with a linear relationship.

a and b are constants.

a is the intercept on the Y-axis (value of Y when X = 0).

b is the slope of the line, i.e.

tan⁡ θ = b

Consumption function of consumers: \[C=\bar{C}+cY\]

Where,

• \[\overline{C}\] is autonomous consumption (autonomous expenditure on consumption).

• c is the marginal propensity to consume (MPC).

Consumption function with intercept \[\overline{C}\]

Graphically, the consumption function is a straight line.

Intercept of consumption function = \[\overline{C}\]

Slope of consumption function is c = tan⁡ α 

A two-sector model has two sources of final demand:

• Consumption
• Investment

Investment function:

\[I = \overline{I}\]

Investment function with I as autonomous

Graphically,

\[I = \overline{I}\]

is a horizontal line at height \[\overline{I}\] above the horizontal axis.

Investment is autonomous, i.e., it remains the same at all income levels.

Aggregate demand shows the total demand (Consumption + Investment) at each level of income.

Aggregate demand is obtained by vertically adding the consumption and investment functions.

Graphically, aggregate demand is obtained by vertical addition of the consumption and investment functions.

• OM = \[\overline{C}\]
• OJ = \[\overline{I}\]
• OL = \[\overline{C}\] + \[\overline{I}\]

The aggregate demand function is parallel to the consumption function because both have the same slope c.

Aggregate demand represents ex ante demand.

Aggregate supply curve with a 45° line.

• In microeconomics, the supply curve has price on the vertical axis and quantity supplied on the horizontal axis.
• In the first stage of macroeconomic theory, the price level is fixed.
• Aggregate supply (GDP) can move up or down smoothly because unused resources are available.
• Whatever the level of GDP, the same amount is supplied; the price level has no role.
• Aggregate supply is represented by a 45° line.
• Every point on the 45° line has equal horizontal and vertical coordinates.
• Example:
• If GDP is ₹1,000 at point A, then ₹1,000 worth of goods is supplied at the corresponding point B on the 45° line.

• Equilibrium is shown by combining ex ante aggregate demand and aggregate supply in one diagram.
• Equilibrium occurs where ex ante aggregate demand equals ex ante aggregate supply.
• Equilibrium point is E.
• Equilibrium level of income is OY₁.

Equilibrium of ex ante aggregate demand and supply

Ex ante aggregate demand: \[AD=\bar{C}+\bar{I}+cY\]

Ex ante aggregate supply:

AS = Y

At equilibrium,

AD = AS

Therefore,

\[\bar{C}+\bar{I}+cY=Y\]

Rearranging,

\[Y(1-c)=\bar{C}+\bar{I}\]

Equilibrium income:

\[Y=\frac{\bar{C}+\bar{I}}{1-c}\]

• Consumption function is a straight line with intercept \[\overline{C}\] and slope c.
• Investment is autonomous and constant at all income levels: \[I = \overline{I}\]
• Aggregate demand is the vertical sum of consumption and investment and is parallel to the consumption function.
• Aggregate supply with fixed price level is represented by a 45° line, where output supplied equals GDP.
• Equilibrium occurs where ex ante aggregate demand equals ex ante aggregate supply, giving equilibrium income OY₁.
• Algebraically, \[Y=\frac{\bar{C}+\bar{I}}{1-c}\]